Informatics and Applications
2024, Volume 18, Issue 4, pp 26-33
STATISTICAL PROPERTIES OF THE MEAN-SQUARE RISK ESTIMATE FOR THE BLOCK THRESHOLD PROCESSING METHOD IN NONPARAMETRIC REGRESSION PROBLEMS WITH A RANDOM GRID
Abstract
Wavelet analysis methods in combination with thresholding procedures are widely used in nonparametric
regression problems when estimating a signal function from noisy data. Their popularity is explained by their
adaptability to local features of the functions under study, high speed of processing algorithms, and optimality of
the estimates obtained. Error analysis of these methods is an important practical task, since it allows one to estimate
the quality of both the methods themselves and the equipment used. Sometimes, the nature of the data is such
that observations are recorded at random points in time. If the sample points form a variation series of a sample
from a uniform distribution over the data recording interval, then the use of standard thresholding procedures is
adequate. This paper considers the block thresholdingmethod, in which the wavelet decomposition coefficients are
processed in groups that allows one to take into account information about neighboring coefficients. An analysis
of the mean square risk estimate of this method is carried out and it is shown that under certain conditions, this
estimate turns out to be strongly consistent and asymptotically normal.
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[+] About this article
Title
STATISTICAL PROPERTIES OF THE MEAN-SQUARE RISK ESTIMATE FOR THE BLOCK THRESHOLD PROCESSING METHOD IN NONPARAMETRIC REGRESSION PROBLEMS WITH A RANDOM GRID
Journal
Informatics and Applications
2024, Volume 18, Issue 4, pp 26-33
Cover Date
2024-12-26
DOI
10.14357/19922264240404
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
wavelets; block thresholding; randomsamples; unbiased risk estimation
Authors
O. V. Shestakov  ,  , 
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov
Moscow State University, 1-52 Leninskie Gory, GSP-1,Moscow 119991, Russian Federation
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
Moscow Center for Fundamental and Applied Mathematics, M. V. Lomonosov Moscow State University,
1 Leninskie Gory, GSP-1,Moscow 119991, Russian Federation
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